a new phenomenon: sub-tg, solid-state, plasticity …web.mit.edu/npdhye/www/padhye-nature-2017.pdfa...

1Scientific RepoRts | 7:46405 | DOI: 10.1038/srep46405

www.nature.com/scientificreports

A New Phenomenon: Sub-Tg, Solid-State, Plasticity-Induced Bonding in PolymersNikhil Padhye1, David M. Parks1, Bernhardt L. Trout2 & Alexander H. Slocum1

Polymer self-adhesion due to the interdiffusion of macromolecules has been an active area of research for several decades. Here, we report a new phenomenon of sub-Tg, solid-state, plasticity-induced bonding; where amorphous polymeric films were bonded together in a period of time on the order of a second in the solid-state at ambient temperatures, up to 60 K below their glass transition temperature (Tg), by subjecting them to active plastic deformation. Despite the glassy regime, the bulk plastic deformation triggered the requisite molecular mobility of the polymer chains, causing interpenetration across the interfaces held in contact. Quantitative levels of adhesion and the morphologies of the fractured interfaces validated the sub-Tg, plasticity-induced, molecular mobilization causing bonding. No-bonding outcomes (i) during the uniaxial compressive straining of films (a near-hydrostatic setting which strongly limits plastic flow) and (ii) between an ‘elastic’ and a ‘plastic’ film further established the explicit role of plastic deformation in this newly reported sub-Tg solid-state bonding.

If two pieces of a glassy polymer are brought into molecular proximity at temperatures well below their glass transition temperature (Tg), negligible adhesion due to interdiffusion of macromolecules will be noted. Because polymer chains are kinetically trapped well below the Tg

1–4, the time scales for relaxations in the glassy state are extremely large5–7. Therefore, the system is essentially frozen with respect to any cooperative segmental motions (α-like relaxation)8 that would cause interdiffusion. The glass transition temperature itself is typically charac-terized by viscosity and diffusivity values of 1013 Poise and 10−24 m2/s, respectively9. Assuming a viscosity of 1013 Poise at the glass transition temperature10, self-diffusion coefficients of forty polymers (at their respective glass-transition temperatures) were estimated to be approximately 10−25 m2/s. Similarly, several other examples of extremely slow kinetics in glass forming liquids near the Tg (marked by very small diffusion coefficients) are reported in the literature11–13.

However, if the two pieces are brought into contact at a temperature above the glass transition temperature, along with the application of moderate contact pressure, polymer chains from the two sides interdiffuse on experimental timescales14–23. As a result of this interdiffusion, there is an optical disappearance of cracks and the development of strong bonds between the two surfaces over time. The strength of the developing interface is a function of temperature, time of healing and contact pressure, and the healing process continues until the inter-face acquires the bulk properties. Typically, for times smaller than the bulk reptation time, the interface tough-ness (Gc) and shear strength (σs) show a monotonic time-dependent growth as Gc ~ t1/2 and σs ~ t1/4 22,24–26. The temperature strongly dictates the molecular mobility, with the self-diffusion coefficient of polymer melts usually ranging between 10−10 and 10−20 m2/s (see Supplementary Table 3). Moderate contact pressures (ranging from 0.1 MPa to 0.8 MPa) have been reported to be essential for facilitating the intimate contact between the interfaces that allows interdiffusion. The chemical structure, the molecular weight and polydispersity of the polymer, the geometry of the joint, and the method of testing are critical factors affecting the measured strength or toughness of the interface.

In the past two decades, there have been reports of evolving polymer adhesion due to interdiffusion at temper-atures somewhat below the bulk Tg, with relatively long healing times of order several minutes27,28, hours29,30, and even up to a day31. Interpretations of such studies have suggested that bonding of a glassy polymer via molecular interdiffusion, even at temperatures below the bulk Tg, is possible over such time scales if a near-surface layer of

1Massachusetts Institute of Technology, Department of Mechanical Engineering, Cambridge, 02139, USA. 2Massachusetts Institute of Technology, Department of Chemical Engineering, Cambridge, 02139, USA. Correspondence and requests for materials should be addressed to N.P. (email: [email protected]) or D.M.P. (email: [email protected]) or B.L.T. (email: [email protected])

received: 06 October 2016

Accepted: 17 March 2017

Published: 20 April 2017

OPEN

mailto:[email protected]



www.nature.com/scientificreports/


the polymer remains in a rubbery state. Evidence of enhanced molecular dynamics characteristic of rubbery-like behavior, taking place within a thin layer at the free surface of an otherwise glassy polymer, has been obtained from both experiments32,33 and computer simulations34. Within near-surface layers, the component of mean mac-romolecular orientation normal to the free surface is suppressed. The resultant effects of entropic and enthalpic factors can lead to segregation or repulsion of chain ends at the free surface35. The segregation of chain ends at the free surface can contribute to the depression of the glass transition temperature at the surface35–38. However, such effects decay within distances from the free surface comparable to the bulk radius of gyration of the polymer.

Although the motion of macromolecules in a glassy state is effectively frozen on short time scales, stress-induced molecular mobility of glasses has been studied since the work of Eyring39. Argon and co-workers40 demonstrated that the case II sorption rates of low molecular weight diluent species into a plastically-deforming glassy poly(ether-imide) were dramatically enhanced, and were comparable with the sorption rates into the poly-mer at Tg, and that plastically-deforming glassy polymers exhibit a mechanically-dilated dynamical state bearing strong similarities to the molecular-level conformational rearrangements taking place at Tg in the absence of active deformation. A related study41 also reported an increase in the case II front velocity (of approximately 6.5 times) when an out-of-surface tensile stress was applied. Lee et al.42 showed that uniaxial deformation of PMMA 19 K below its Tg exhibited an increased molecular mobility by up to 1000 times. Loo et al.43 used NMR to probe deuterated semi-crystalline Nylon 6 and reported enhanced conformational dynamics in the amorphous regions of Nylon when deformation was carried out near Tg. Molecular dynamics simulations44 also revealed increased torsional transition rates and thus enhanced molecular mobility during active deformation of a glass. The plastic deformation of glassy polymers is understood in terms of localized step-like shear cooperative displacements of lengthy chain segments, and the unit plastic rearrangements are known as shear transformations45. According to molecular dynamics simulations46, slippage of chains is the underlying feature of a shear transformation (for a detailed discussion, see Supplementary Section 3.2). Here, we report that active plastic deformation of glassy polymeric films held in intimate contact can trigger requisite molecular-level rearrangement sufficient to cause interpenetration of polymer chains across the interface, which leads to bonding. Figure 1 compares and contrasts cases of polymer self-adhesion through interdiffusion with the plasticity-induced bonding mechanism proposed herein.

ResultsFigure 2 illustrates the preparation of polymeric films by solvent casting using a base polymer (hydroxypro-pyl methylcellulose) and a plasticizer (polyethylene glycol, PEG-400). The base polymer HPMC was available under the trade name METHOCEL in E3 and E15 grades. The molecular structures of the polymer and plasti-cizer are shown in Fig. 3. Films of varying composition were prepared and assigned unique names characteriz-ing base polymer and weight percent (wt.%) of the plasticizer in the film with respect to the base polymer (see Methods and Supplementary Section 1). Films made from E3-alone-42.3% PEG, E3/E15 in 1:1–42.3% PEG and E15-alone-42.3% PEG exhibited Tg-values in the range of 72–78 °C. (See Methods and Supplementary Section 2.2). Their ambient-temperature tensile true stress-strain curves are shown in Fig. 4. All three films exhibited ductility, represented by their ability to undergo plastic flow.

Figure 1. Schematic illustration contrasting mechanisms of interface molecular interpenetration (a) Polymer self-adhesion generated by molecular diffusion at temperatures near or above Tg. (b) Newly-proposed sub-Tg, solid-state, plasticity-induced bonding in which bulk plastic deformation triggers the requisite molecular mobility for chain interpenetration across the interfaces.



Bonding experiments were carried out at ambient conditions (18° ± 2 °C). (i) Stacks of six film layers, each of thickness ~100 μm, were fed through a roll-bonding machine to achieve active plastic deformation at ambi-ent temperatures over time intervals on the order of a second (see Supplementary Table 4 for estimates of the active deformation times due to rolling). Symmetric peel tests were performed to measure the mode I fracture toughness (Gc [J/m2 ]), Fig. 5, and (ii) lap specimens were prepared to measure the shear-strength (σs [MPa]), Fig. 6. (See Methods and Supplementary Section 4 for details on roll-bonding, peel testing and lap shear strength testing). Gc represents the work done per unit area for debonding the interface during a peel test. σs indicates the maximum nominal shear stress sustained by the bonded interface before failure. The effective thickness reduction was used as a measure of plastic strain during bonding in all of the cases.

Figure 2. Steps involved in the preparation of polymer films through solvent casting: (a) homogeneous solution of polymer and plasticizer in ethanol and water, (b) spreading of the solution on a glass surface via a knife, and (c) evaporation of solvents and formation of a glassy film after drying.

Figure 3. Molecular structures of hydroxypropyl methylcellulose (HPMC) and polyethylene glycol (PEG).

Figure 4. Ambient-temperature tensile true stress- true strain curves for three film formulations: E3-alone-42.3% PEG, E3/E15 in 1:1–42.3% PEG and E15-alone-42.3% PEG. The nominal strain rate for tensile testing was 0.0025 sec−1.



Figure 7 illustrates the consolidation of several layers of the film (E3/E15 in 1:1–42.3% PEG) comprising an initial thickness of t1 = 0.60 mm, which undergoes roll-bonding through active plastic deformation, emerging from the process with an integral final thickness reduced to t2 = 0.533 mm (see Supplementary video S1).

Figure 8 shows Gc results for the three films. Gc correlates with the imposed plastic strain in a non-monotonic fashion, first increasing and then decreasing. The adhesion between two interfaces held together by van der Waals forces, hydrogen bonds, or chemical bonds can only give Gc values in the range of 0.05 J/m2. 0.1 J/m2 and 1.0 J/m2,

Figure 5. (a) Roll-bonding was achieved by passing a stack of film layers with a total initial thickness t1 between compression rollers to yield a final-thickness t2. (b) The peel-test was carried out on a roll-bonded sample, forcing delamination at the middle interface.

Figure 6. Lap specimens were prepared between two film layers. (a) Application of compression loads on the overlapping area (A) to cause plastic deformation. Initial thickness (t1) is reduced to (t2). (b) Lap shear-strength measurements were performed in a tensile mode.

Figure 7. Illustration of sub-Tg, solid-state, plasticity-induced roll-bonding of E3/E15 in 1:1–42.3% PEG films nearly 60 K below Tg. For this case, the nominal thickness strain is ep = |t2 − t1|/t1 = 11.7%.



respectively47. The surface energy of glassy polymers itself is quite small48 (on the order of 0.08 J/m2); therefore, negligible adhesion is noted when two such surfaces are brought into mere molecular proximity. However, glassy polymers can exhibit higher fracture toughness owing to the irreversible deformation of the macromolecules. Thus, the quantitative levels of interface toughness Gc obtained here, with a maximum value nearly 10 J/m2, can be attributed to the irreversible processes of chain pull-outs, disentanglement and/or scissions during debonding, which could only happen if plasticity-induced molecular mobilization and chain-interpenetration had led to bonding. It is worth emphasizing that studies on polymer adhesion leading to Gc values up to 1.2 J/m2 and 2.0 J/m2, respectively31,49, have attributed such levels of fracture toughnesses due to chain interdiffusion and irrevers-ible chain pull-out mechanisms during debonding. The levels of fracture toughnesses reported in our study are comparably larger than those reported in these studies, and therefore affirm that in our case bonding occured via chain interpenetration and debonding involves irreversible chain pull-out processes. Other mechanisms of adhesion such as acid-base interactions, capillary effects, electrostatic forces and/or any other conceivable mech-anism do not apply in the current context (for a detailed discussion on the types of forces giving rise to adhesion, see ref. 50). The lap shear strength (σs) data, shown in Fig. 9, also exhibits a similar non-monotonic correlation with the bonding plastic strain. Quantitative levels of the σs values reported here compare with certain experi-mental results reported in the literature29, in which adhesion due to interdiffusion of chains up to 50 K below the bulk Tg over long times (on the order of several minutes) was reported. The reported levels of bulk plastic strains necessary for bonding also rule out any major role of mechanical interlocking of asperities to cause adhesion; at the levels of plastic strains reported here, surface asperities would necessarily flatten out. Surface characterization of the films through AFM, before bonding, revealed nano-scale roughness (Ra) on the order of 6.91–22.7 nm (see Supplementary Section 2.5). By contrast, increasing levels of plastic strain lead to asymptotically-increasing contact areas, and if factors other than chain interpenetration were responsible for bonding, we would expect a monotonic increase in Gc or σs. The decrease of Gc or σs at high levels of plastic strain could plausibly be explained on the basis of deformation-induced anisotropy in the near-interface chain orientation distribution. We suggest

Figure 8. Fracture toughness (Gc [J/m2]) versus plastic strain plots for E3/E15 in 1:1–42.3%PEG, E3-alone-42.3%PEG and E15-alone-42.3%PEG. The Gc values are based on the mean steady-state force during peeling and the error bars in Gc correspond to fluctuations during steady-state peeling. Plastic strain is calculated based on 10 mean thickness measurements before and after bonding, and the error bars in plastic strain are derived from these measurements. The error bars in Gc and plastic strain represent uncertainty of one standard deviation.

Figure 9. Lap shear-strength (σs [MPa]) versus plastic strain plots for E3/E15 in 1:1–42.3%PEG, E3-alone-42.3%PEG and E15-alone-42.3%PEG. Plastic strain is calculated based on mean thicknesses before and after bonding (10 measurements), and the error bars in plastic strain are derived from these measurements. The error bars on plastic strain represent uncertainty of one standard deviation.



that increasing plastic strain ultimately causes increasing chain orientation parallel to the rolling direction (max-imum principal stretch direction) that leads to less effective chain interpenetration across the interface, serving to reduce the degree of bonding at higher strains. We also studied the effect of strain-rate on roll-bonding of laminates and found that fracture toughness again correlated primarily with plastic strain, showing negligible strain-rate sensitivity (see Supplementary Figure 20 and discussion in Section 5).

Figure 10 shows a comparison of representative surface morphology before bonding and after the fracture. The debonded fracture surfaces indicate local sites of chain scissions or pull-outs due to fracture. Such features are similar to those reported upon fracture of polymers welded through interdiffusion22,28,51.

To explicitly demonstrate the role of bulk plastic deformation in bonding, we designed a ‘uniaxial die’ setup, which was capable of imposing uniaxial strain and strongly limiting the magnitude of macroscopic plastic flow. Figure 11 shows a comparison in which a stack of films (E3/E15 in 1:1–42.3% PEG) was compressed (i) with-out any constraints and (ii) with the ‘uniaxial die’ constraint. In both cases, the stack of films were subjected to same level of peak nominal compressive stress of 78.98 MPa for a short time interval on the order of a second. (See Supplementary Section 4.5 for deformation analyses and details). In the first case (simple upsetting), the stack underwent macroscopic compressive plastic flow, and the layers bonded to form an integral structure (see Supplementary video S2-a), whereas in the case of the ‘uniaxial die’ constraint, no permanent thickness change or plastic strain was observed, and the layers readily splayed apart after removal from the die (see Supplementary video S2-b part I, part II and part III).

In another experiment, we attempted to roll-bond E3/E15 in a 1:1–0% PEG film with E3/E15 in a 1:1–42.3% PEG film (see Supplementary video S3) and a no-bonding outcome was noted. Films with 0% PEG have high flow strengths, and exhibit negligible plastic flow (see Supplementary Fig. 1(a)) when tested in tension. When attempting to roll-bond high-strength laminae to those of much lower flows strength, essentially all plas-tic deformation localizes within the lower-strength material. Because the higher-strength material remained glassy and non-deforming during rolling, it was therefore incapable of either contributing or incorporating any plasticity-mobilized chain segments across the interface, again leading to non-bonding results. Nanoindentation experiments were performed on E3/E15 in 1:1–0% PEG, E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG and E15-alone-42.3% PEG films. The indentation experiments were carried out in a force controlled mode with a maximum force of 2000 μN and 300 μN for 0% PEG and 42.3% PEG films, respectively. A larger load for the 0% PEG film was chosen in order to activate sufficient plastic indentation so that its hardness could be measured. Berkovich indenter with a root radius of 150 nm was used. The load versus displacement curves for all the films are shown in the Fig. 12. The film with 0% PEG shows a relatively large indentation force and large elastic recov-ery, whereas films with 42.3% PEG films show little elastic recovery and large residual indentation depth. Based

Figure 10. SEM images of E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG, and E15-alone-42.3% PEG, films before bonding and after debonding. The nominal plastic strains during roll-bonding for E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG, and E15-alone-42.3% PEG, films were 15.53%, 8.12%, and 10.18%, respectively.



on these relative behaviors, the 0% PEG film can be called an ‘elastic’ film and the 42.3% PEG film as a ‘plastic’ film. Using Oliver-Pharr method we estimated the hardness from the nano-indentation tests. The hardness values for E3/E15 in 1:1–0% PEG, E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG and E15-alone-42.3% PEG films were 144.0 ± 0.39 MPa, 10.83 ± 0.03 MPa, 10.151 ± 0.15 MPa, and 11.48 ± 0.39 MPa, respectively. The bar graph in Fig. 13 compares the hardness values of these films. This also confirmed, that at a given load, films with 0% PEG are “hard” and unlikely to demonstrate plasticity-induced molecular mobilization for bonding, whereas 42.3% PEG films can exhibit substantial plastic flow.

DiscussionWhen the temperature of a glass-forming liquid is lowered and the glass transition temperature is approached from above, kinetics of a glass-forming system shows a drastic slow-down, and time scales for relaxations increase by orders of magnitude to allow any appreciable diffusion in experimental timescales. The classic Bueche-Cashin-Debye equation52,53, which relates diffusivity and viscosity, is given as:

Figure 11. Compression of stacks of films (a) without any die containment to permit macroscopic plastic flow and bonding, (b) in a ‘uniaxial strain die’ that is capable of limiting the plastic flow, and consequently no bonding takes place. In both cases peak nominal compressive stresses (78.98 MPa) was kept same.

Figure 12. Illustration on load versus displacement curves in nanoindentation for E3/E15 in 1:1–0% PEG, E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG and E15-alone-42.3% PEG films. Indentation experiments were carried out in load controlled mode with chosen peak loads up to 300 μN and 2000 μN for films with 42.3% PEG and 0% PEG, respectively.



ηρ=

D AK T RM36 (1)

B2

In the above equation, A is the Avogadro constant, KB is the Boltzmann constant, T is the absolute tempera-ture, R2 is the mean-square end-to-end distance of a single polymer chain, and M is the molecular weight. If we estimate D for our polymer at the glass-transition temperature by considering η = 1013 Poise, ρ = 1180 Kg/m3, R2 = 6 × 7.42 nm2 (using Rg of E3, and R2 = 6 × Rg

2) and M = 20,300 g/mol (See Supplementary Section 2.3 for molecular properties), and T = Tg = 352 K, the estimated value of D is 1.12 × 10−24 m2/s. This is a remarkable estimate in terms of the order of magnitude and compares well with the reported10 self-diffusivity of 10−25 m2/s. If we consider a scenario: in which a diffusion distance of x = 10 nm is to be achieved within a time interval of one second, then D(= x2/2t) must be greater than 0.5 × 10−16 m2/s. This is not possible in the solid-state, 60 K below the bulk-Tg, and clarifies the distinction of polymer welding above Tg with respect to newly reported plasticity-induced molecular mobilization and bonding which occurred in a period of time on the order of a second.

Quantitative levels of bonding reported in this paper and their correlations with bulk plastic deformation and fracture surface morphology imply molecular mobilization and chain interpenetration across the interface as the mechanism of bonding. Furthermore, no-bonding outcomes in the ‘uniaxial die’ experiment and between an ‘elastic’ and a ‘plastic’ film emphasize that even effects associated with the presence of a rubbery-like layer of higher molecular mobility within a molecular thin layer near the surface, could not provide adhesion of the mag-nitude observed during contacts lasting on the order of a second at 50 C below Tg. Both these experiments explic-itly demonstrated that activating bulk plastic flow on both sides of the interface was an essential requirement for bonding. Bonding below the bulk Tg (without any bulk plastic deformation), as reported in the literature, requires substantially longer durations. Additionally, the existence of any enhanced relaxation of the polymer chains (or segments) in the surface layer would be severely restricted by any portions of the macromolecules extending into the glassy-bulk beneath; hence, long-range diffusion within a short time is not possible. Finally, although not considered in these prior reports, it is plausible that moderate contact pressures, applied over relatively long healing times at temperatures near Tg, may have contributed to mechanically enhanced molecular mobility that contributed to bonding via mechanisms similar to those described here.

We emphasize that the kinetically trapped state of a molecular glass implies that any cooperative segmental relaxations or long range diffusive motions of chains are severely restricted; however, secondary relaxation pro-cesses (those corresponding to vibrations of side groups like β, γ, δ, etc. relaxations) may still be active. But, such weak secondary relaxation processes are incapable of giving any appreciable molecular interdiffusion and pro-nounced adhesion in a short-time (fraction of a second), when two interfaces are brought together in molecular proximity, unless enhanced mobility is triggered through plastic deformation.

Although rapid plastic deformation can cause a temperature rise, at relatively slow strain-rates the associated temperature rise is negligible. A fully adiabatic analysis revealed an upper bound temperature increase of only 3.6 °C (see Supplementary Section 3.3). The mechanically activated polymer mobility well below Tg is mechanisti-cally quite different from molecular mobility at temperatures above Tg, and the key differences can be summarized as follows: Diffusion primarily occurs due to high kinetic energy of the polymer chains (or segments), and avail-able free-volume (or physical space) due to which chains (or segments) can sample new orientations effectively. The polymer melts (above Tg) are spatially homogeneous and in a thermodynamic equilibrium state, whereas, plastic deformation and associated enhanced mobility in a glassy polymer is not at all an equilibrium concept. The root mean square displacement of center of mass of a polymer chain will increase monotonically with time dur-ing diffusion in a polymer melt, however, the mechanically assisted enhanced mobility in polymers only occurs during active plastic deformation and effectively ceases when plastic straining stops. The average kinetic energy of a polymer molecule is large in a polymer melt compared to that in the solid-state glass well below Tg. Finally,

Figure 13. Hardness measurements for E3/E15 in 1:1–0% PEG, E3/E15 in 1:1–42.3% PEG, E3-alone-42.3% PEG and E15-alone-42.3% PEG films. Nanoindentation experiments were conducted on film surfaces of size 1 × 1 mm2 and the mean hardness over 51 measurements is shown. The error bars represent uncertainty of one standard deviation.



the self-diffusion coefficient (D) of a polymer chain in its melt state shows a strong dependence on the molecular weight, D ~ M−1 or D ~ M−2 in accordance with the Rouse or the reptation model, respectively. However, all three blends of polymer considered here, E3-alone, E15-alone and E3/E15 in 1:1, were roll-bonded in time intervals on the order of a second, which, owing to the large differences in molecular weight among the blends, is in significant contrast from the mechanism of polymer adhesion due to interdiffusion. We speculate that shear transformation units of plastic deformation accompanied by local transient dilatations (volume changes) could facilitate oppor-tunities for establishing entanglements across the interface, such that plasticity-induced bonding can take place in a period of time on the order of a second at temperatures many tens of degrees below bulk Tg. Novel insights associated with the newly reported phenomena and proposed underlying mechanisms are expected to open new avenues for research and applications. Particularly, detailed mechanistic understanding of deformation induced polymer mobility causing bonding at the interface and their dependence on strain-rate, temperature etc. are worthwhile pursuits.

MethodsFilm-Making. Hydroxypropyl methyl cellulose (HPMC), trade name METHOCEL, in grades E3 and E15 was obtained from Dow Chemical (Midland, Michigan, North America). PEG-400 was purchased from Sigma-Aldrich (Milwaukee, Wisconsin, North America). Appropriate amounts of E3, E15 and PEG were mixed in desired amounts with ethanol and water, and a homogeneous solution was obtained through mixing with an electric stirrer for 24 h. After completion of the blending process, the solution was carefully stored in glass bot-tles at rest for 12 h to eliminate air bubbles. Solvent casting was carried out using a casting knife applicator from Elcometer (Rochester Hills, Michigan, North America) on heat-resistant borosilicate glass. All of the steps were carried out in a chemical laboratory where ambient conditions of 18° ± 2 °C and R.H. 20 ± 5% were noted. The residual moisture content in the films after drying was measured using Karl Fischer titration.

Bonding Experiments. Roll bonding was carried out on a machine capable of exerting the desired load levels to achieve active plastic deformation. A pair of 200 mm diameter rollers were driven at an angular speed of 0.5 rev/min, leading to an exit speed of 5.23 mm/s. Peel tests were carried out to measure mode I fracture toughness (see Supplementary video S4). Lap specimens were prepared using compression platens on an Instron mechanical tester. For both roll-bonded and lap specimens, for the sake of consistency, the adhesion measure-ments were carried out on the bonded interfaces between the top-top surfaces (exposed side during drying). Film layers were stacked accordingly. Top-bottom and bottom-bottom joining led to similar bonding results. The ‘uni-axial die’ and ‘upsetting’ experiments were carried out on the Instron. The roll-bonding machine and fixture for the peel test were designed and fabricated in Massachusetts Institute of Technology (Cambridge, North America) (see Supplementary Section 4).

Characterization. The molecular weights of E3 and E15 were estimated from viscosity measurements. The amorphous nature of the films were verified by XRD. SEM and AFM were performed to analyze the surfaces. DMA was performed to determine the Tg. Tensile stress-strain curve tests, fracture toughness through peel tests, and lap shear tests were carried out. Nanoindentation was carried out to measure the hardness. The specific heat capacity was measured using DSC.

X-ray diffraction was conducted using a PANalytical X’Pert PRO Theta/Theta powder X-ray diffraction sys-tem with a Cu tube and an X’Celerator high-speed detector. AFM images were obtained using a Dimension 3100 XY closed loop scanner (Nanoscope IV, VEECO) equipped with NanoMan software. Height and phase images were obtained in tapping mode in ambient air with silicon tips (VEECO). DMA was carried out on a TA Q800 instrument. Mechanical testing was performed on an Instron mechanical tester. Nanoindentation tests were car-ried out on a Triboindenter Hysitron instrument. Calorimetry was performed on a TA Q200 instrument. The viscosity was measured on an HR-3 Hybrid rheometer54.

References1. Alegria, A., Guerrica-Echevarria, E., Goitiandia, L., Telleria, I. & Colmenero, J. Alpha-relaxation in the glass transition range of

amorphous polymers. 1. temperature behavior across the glass transition. Macromolecules 28, 1516–1527 (1995).2. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001).3. Ediger, M., Angell, C. & Nagel, S. R. Supercooled liquids and glasses. J. Phys. Chem. 100, 13200–13212 (1996).4. Stillinger, F. H. A topographic view of supercooled liquids and glass formation. Science 267, 1935–1939 (1995).5. Colby, R. H. Dynamic scaling approach to glass formation. Phys. Rev. E 61, 1783 (2000).6. Hutchinson, J. M. Physical aging of polymers. Prog. Polym. Sci. 20, 703–760 (1995).7. Jerome, B. & Commandeur, J. Dynamics of glasses below the glass transition. Nature 386, 589–592 (1997).8. Angell, C. A., Ngai, K. L., McKenna, G. B., McMillan, P. F. & Martin, S. W. Relaxation in glassforming liquids and amorphous solids.

J. Appl. Phys. 88, 3113–3157 (2000).9. Smith, R. S. & Kay, B. D. Breaking through the glass ceiling: Recent experimental approaches to probe the properties of supercooled

liquids near the glass transition. J. Phys. Chem. Lett. 3, 725–730 (2012).10. Lee, L.-H. Adhesion of high polymers. i. influence of diffusion, adsorption, and physical state on polymer adhesion. J. Polymer Sci.

2 Polymer Phys. 5, 751–760 (1967).11. Swallen, S. F., Urakawa, O., Mapes, M. & Ediger, M. D. Self-diffusion and spatially heterogeneous dynamics in supercooled liquids

near tg in AIP Conference Proceedings vol. 708, 491–495 (AIP Publishing, 2004).12. Mapes, M. K., Swallen, S. F. & Ediger, M. Self-diffusion of supercooled o-terphenyl near the glass transition temperature. J. Phys.

Chem. B 110, 507–511 (2006).13. Richert, R. & Samwer, K. Enhanced diffusivity in supercooled liquids. New J. Phys. 9, 36 (2007).14. Voyutskii, S. & Vakula, V. The role of diffusion phenomena in polymer-to-polymer adhesion. J. Appl. Polym. Sci. 7, 475–491 (1963).15. Kausch, H. H. & Tirrell, M. Polymer interdiffusion. Annu. Rev. Mater. Sci. 19, 341–377 (1989).16. Prager, S. & Tirrell, M. The healing process at polymer-polymer interfaces. J. Chem. Phys. 75, 5194–5198 (1981).17. Jud, K. & Kausch, H. Load transfer through chain molecules after interpenetration at interfaces. Polym. Bull. 1, 697–707 (1979).


1 0Scientific RepoRts | 7:46405 | DOI: 10.1038/srep46405

18. Jud, K., Kausch, H. & Williams, J. Fracture mechanics studies of crack healing and welding of polymers. J. Mater. Sci. 16, 204–210 (1981).

19. Brown, H. The adhesion between polymers. Annu. Rev. Mater. Sci. 21, 463–489 (1991).20. De Gennes, P.-G. The formation of polymer/polymer junctions. Tribology S. 7, 355–367 (1981).21. Wool, R. & O’connor, K. A theory crack healing in polymers. J. Appl. Phys. 52, 5953–5963 (1981).22. Wool, R. P. Polymer Interfaces: Surface and Strength (Hanser Press: New York, 1995).23. Klein, J. Interdiffusion of polymers. Science 250, 640–646 (1990).24. Kline, D. & Wool, R. Polymer welding relations investigated by a lap shear joint method. Polym. Eng. Sci. 28, 52–57 (1988).25. Cho, B.-R. & Kardos, J. L. Consolidation and self-bonding in poly (ether ether ketone)(peek). J. Appl. Polym. Sci. 56, 1435–1454

(1995).26. Kunz, K. & Stamm, M. Initial stages of interdiffusion of pmma across an interface. Macromolecules 29, 2548–2554 (1996).27. Roy, S., Yue, C., Wang, Z. & Anand, L. Thermal bonding of microfluidic devices: Factors that affect interfacial strength of similar and

dissimilar cyclic olefin copolymers. Sensor Actuat. B-Chem. 161, 1067–1073 (2012).28. Boiko, Y. M. & Prud’Homme, R. E. Strength development at the interface of amorphous polymers and their miscible blends, below

the glass transition temperature. Macromolecules 31, 6620–6626 (1998).29. Boiko, Y. M. Is adhesion between amorphous polymers sensitive to the bulk glass transition? Colloid Polym. Sci. 291, 2259–2262

(2013).30. Boiko, Y. M., Zakrevskii, V. A. & Pakhotin, V. A. Chain scission upon fracture of autoadhesive joints formed from glassy poly

(phenylene oxide). J. Adhesion 90, 596–606 (2014).31. Boiko, Y. M. On the formation of topological entanglements during the contact of glassy polymers. Colloid Polym. Sci. 290,

1201–1206 (2012).32. Meyers, G. F., DeKoven, B. M. & Seitz, J. T. Is the molecular surface of polystyrene really glassy? Langmuir 8, 2330–2335 (1992).33. Fakhraai, Z. & Forrest, J. Measuring the surface dynamics of glassy polymers. Science 319, 600–604 (2008).34. Mansfield, K. F. & Theodorou, D. N. Molecular dynamics simulation of a glassy polymer surface. Macromolecules 24, 6283–6294

(1991).35. Jones, R. Interfaces in The Physics of Glassy Polymers (eds Haward, R. N. & Young, R. J.) 413–450 (Springer, 1997).36. Mayes, A. M. Glass transition of amorphous polymer surfaces. Macromolecules 27, 3114–3115 (1994).37. de Gennes, P.-G. Mechanical properties of polymer interfaces in Physics of Polymer Surfaces and Interfaces (eds Sanchez, I. C. &

Fitzpatrick, L. E.) 55–71 (Butterworth-Heinemann Boston, 1992).38. de Gennes, P.-G. Tension superficielle des polymères fondus. Comptes rendus de l’Académie des sciences. Série 2, Mécanique, Physique,

Chimie, Sciences de l’univers, Sciences de la Terre 307, 1841–1844 (1988).39. Eyring, H. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283–291 (2004).40. Zhou, Q.-Y., Argon, A. & Cohen, R. Enhanced case-ii diffusion of diluents into glassy polymers undergoing plastic flow. Polymer 42,

613–621 (2001).41. Argon, A., Cohen, R. & Patel, A. A mechanistic model of case ii diffusion of a diluent into a glassy polymer. Polymer 40, 6991–7012

(1999).42. Lee, H.-N., Paeng, K., Swallen, S. F. & Ediger, M. Direct measurement of molecular mobility in actively deformed polymer glasses.

Science 323, 231–234 (2009).43. Loo, L. S., Cohen, R. E. & Gleason, K. K. Chain mobility in the amorphous region of nylon 6 observed under active uniaxial

deformation. Science 288, 116–119 (2000).44. Capaldi, F. M., Boyce, M. C. & Rutledge, G. C. Molecular response of a glassy polymer to active deformation. Polymer 45, 1391–1399

(2004).45. Argon, A. S. The Physics of Deformation and Fracture of Polymers (Cambridge University Press, 2013).46. Strelnikov, I., Balabaev, N., Mazo, M. & Oleinik, E. Analysis of local rearrangements in chains during simulation of the plastic

deformation of glassy polymethylene. Polym. Sci. Ser. A+ 56, 219–227 (2014).47. de Gennes, P.-G. Soft Interfaces: The 1994 Dirac Memorial Lecture (Cambridge University Press, 2005).48. Brogly, M., Fahs, A. & Bistac, S. Assessment of nanoadhesion and nanofriction properties of formulated cellulose-based biopolymers

by afm in Scanning Probe Microscopy in Nanoscience and Nanotechnology 2 (ed. Bhushan, B.) 473–504 (Springer Berlin Heidelberg, 2011).

49. Washiyama, J., Kramer, E. J., Creton, C. F. & Hui, C.-Y. Chain pullout fracture of polymer interfaces. Macromolecules 27, 2019–2024 (1994).

50. Lee, L.-H. Fundamentals of Adhesion (Springer, 1991).51. Creton, C., Kramer, E. J., Brown, H. R. & Hui, C.-Y. Adhesion and fracture of interfaces between immiscible polymers: from the

molecular to the continuum scale in Molecular Simulation Fracture Gel Theory 53–136 (Springer, 2002).52. Bueche, F., Cashin, W. & Debye, P. The measurement of self-diffusion in solid polymers. J. Chem. Phys. 20, 1956–1958 (1952).53. Bueche, F. Viscosity, self-diffusion, and allied effects in solid polymers. J. Chem. Phys. 20, 1959–1964 (1952).54. Schaber, S. D. et al. Economic analysis of integrated continuous and batch pharmaceutical manufacturing: a case study. Ind. Eng.

Chem. Res. 50, 10083–10092 (2011).

AcknowledgementsThe authors acknowledge the funding from Novartis Pharma AG and facilities at the Novartis-MIT Center for Continuous Manufacturing program where this research was carried out. First author appreciates discussions with Professor Robert E. Cohen.

Author ContributionsN.P. conducted experiments, designed and developed the experimental set-ups, machines and test-fixtures, and wrote the letter and supplementary. D.M.P. identified and proposed the sub-Tg, solid-state, plasticity-induced bonding and provided supervision on the subject of polymers and mechanics. B.L.T. advised on the phenomenological aspects of adhesion and supervised the overall development of thin-film technology at MIT. A.H.S. supervised the design and development of mechanical fixtures and machines. D.M.P., B.L.T. and A.H.S. jointly supervised the work. All authors contributed to review of the manuscript, and participated in discussions during this research.

Additional InformationSupplementary information accompanies this paper at http://www.nature.com/srepCompeting Interests: The authors declare no competing financial interests.

http://www.nature.com/srep


1 1Scientific RepoRts | 7:46405 | DOI: 10.1038/srep46405

How to cite this article: Padhye, N. et al. A New Phenomenon: Sub-Tg, Solid-State, Plasticity-Induced Bonding in Polymers. Sci. Rep. 7, 46405; doi: 10.1038/srep46405 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license,

unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ © The Author(s) 2017

http://creativecommons.org/licenses/by/4.0/

Supplementary Material forA New Phenomenon: Sub-Tg, Solid-State,Plasticity-Induced Bonding in Polymers

Nikhil Padhye, David M. Parks, Bernhardt L. Trout, Alexander H. Slocum

1 SUPPLEMENTARY FILM-MAKING

Table 1: Formulations employed in making polymer films from HPMC E3 and E15with different levels of plasticizer (the amounts have been rounded off to nearestgrams).

Polymer film CompositionE3 E15 Water EtOH PEG(g) (g) (g) (g) (g)

E3/E15 in 1:1-0% PEG 15 15 96 96 0E3/E15 in 1:1-28.5% PEG 15 15 96 96 12E3/E15 in 1:1-42.3% PEG 15 15 96 96 22E3/E15 in 1:1-59.5% PEG 15 15 96 96 44E3-alone-42.3% PEG 30 0 96 96 22E15-alone-42.3% PEG 0 30 96 96 22

Table 1 shows the sample weights of the contents used in preparation of the solu-tions. As seen in Table 1, films are referred to based on the amounts of E3, E15 andWt.% of PEG-400. For example, E3/E15 in 1:1-42.3% PEG implies that E3 and E15are present in one-to-one ratio and the Wt.% of PEG in the film is 42.3%, since 22 gPEG in 15 g E3 plus 15 g E15 is 42.3%.

Karl Fischer titration was carried out to determine the residual moisture contentin the films after drying. Dimethyl sulfoxide (DMSO) was purchased from SigmaAldrich (ACS reagent grade) and used as a reagent for dissolving films.The solutionof the dissolved film in DMSO was fed into the Karl Fischer Titrator, and the residualmoisture was estimated. Table 2 shows the average amounts (repeated three times) ofthe estimated residual moisture contents in the films.

1

Table 2: Residual moisture in films after drying, measured through Karl Fischertitration. %Wt. indicates residual moisture in the films after drying.

Polymer film Residual H2O(%Wt.)

E3/E15 in 1:1-0% PEG 3.70E3/E15 in 1:1-28.5% PEG 7.21E3/E15 in 1:1-42.3% PEG 4.29E3/E15 in 1:1-59.5% PEG 2.45E3-alone-42.3% PEG 2.92E15-alone-42.3% PEG 4.54

2 SUPPLEMENTARY CHARACTERIZATION

2.1 Role of Plasticizer and Mechanical Properties

0

5

10

15

20

25

30

35

40

45

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Stre

ss (

MPa

)

Strain

E3/E15 in 1:1-0% PEG

E3/E15 in 1:1-28.5% PEG

E3/E15 in 1:1-42.3% PEG

E3/E15 in 1:1-58.5% PEG

(a)

PEG 400

(b)

Figure 1: (a) Effect of PEG-400 on tensile true stress-strain behavior of polymericfilms. The tensile tests were carried out at ambient temperature and a nominalstrain rate of 0.0025 s−1. (b) Schematic role of plasticizer on molecular configura-tions.

Figure 1(a) shows true stress-strain behavior of films made from E3/E15 in 1:1with varying the PEG concentrations 0%, 28.5%, 42.3% and 59.5%, respectively. The

2

(a) E3/E15 in 1:1-0% PEG (b) E3/E15 in 1:1-28.5% PEG

(c) E3/E15 in 1:1-42.3% PEG (d) E3/E15 in 1:1-58.5% PEG

(e) E3-alone-42.3% PEG (f) E15-alone-42.3% PEG

Figure 2: Dynamic Mechanical Analysis Curves.

plasticization effect of increasing PEG (Wt.%) is evidenced by the lowering of theinitial modulus and the yield strength and, increase in the failure strain. The maximumfailure strain occurs for 42.3% PEG film. Clearly, all films containing PEG demonstratelarge ductility that is absent in 0% PEG film.

2.2 Dynamic Mechanical AnalysisDynamic Mechanical Analysis was performed on all the films listed in Table 1. Atemperature sweep was performed at 1 Hz frequency. Figures 2(a) to 2(f), showthe plots of loss modulus, storage modulus and tan δ for six different films. The glasstransition temperature is determined by the peak in the tan δ. For E3-alone-42.3% PEGTg was estimated to be 72◦ C, and for E15-alone-42.3% PEG and E3/E15 in 1:1-42.3%PEG Tg was estimated as 78◦ C. Inclusion of PEG evidently lowers the glass transitiontemperature and broadens the temperature range over which the glass transition takesplace.

3

2.3 Molecular Weight

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 100 200 300 400 500 600

Vis

cosi

ty (

Pa-s

)

Strain-rate (sec-1)

HPMC E3

HPMC E15

Figure 3: Viscosity curves of 2% aqueous solution of METHOCEL-E3 andMETHOCEL-E15.

Viscosity measurements for 2% aqueous solution of E3 and E15 were carried outbased on the procedure prescribed by Dow [2]. The viscosity curves for E3 and E15are shown in the Figure 3. If we choose a representative viscosity of 3.8 mPa-s forE3 and 16 mPa-s for E15, then based on the viscosity and molecular weight relation-ship from [1], we estimate the number average molecular weight (Mn) for E3 and E15approximately as 8,200 and 20,000, respectively.

A detailed molecular characterization of METHOCEL cellulose ethers presented in[14], also led to estimation of weight average (Mw) and number average (Mn) molecularweights as: (i) E3: Mn = 8,100 and Mw = 20,300 with Mw/Mn = 2.5, and (ii) E15:Mn = 24,800 and Mw = 60,300 with Mw/Mn = 2.4. Such estimations are consistentwith those we obtained. In the same study [14], the degree of polymerization (DP) wasreported as: (i) E3, DP= 77, and (ii) E15, DP=296, and the weight average radius ofgyration (Rgw) as: (i) E3, Rgw = 7.4 nm, and (ii) E15, Rgw = 15.1 nm.

2.4 X-Ray DiffractionHPMC is a cellulose derivative and well known to exist in amorphous form. As anillustration, XRD pattern of E3/E15 in 1:1-42.3% PEG is shown in Figure 4. Asexpected, a diffused pattern without any peaks is obtained, thus, indicating absence ofany crystallinity.

2.5 Atomic Force MicroscopyFigure 5 shows sample AFM scans of a 5 µm x 5 µm area on the top surface of threefilms with 42.3% PEG, along with the average roughness given by Ra.The top surfacesof films exhibit nano-scale roughness, however, this scale of roughness does not playany important role when we have reported bulk plastic strains essential for bonding.

4

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25 30 35 40 45

Inte

nsi

ty

2θ (°)

HPMC E3/E15 in 1:1-42.3% PEG

Figure 4: XRD of E3/E15 in 1:1-42.3% PEG.

(a) Top surface of E3/E15 in1:1-42.3% PEG film, Ra = 6.91nm

(b) Top surface of E3-alone-42.3% PEG film, Ra = 22.7 nm

(c) Top surface of E15-alone-42.3% PEG film, Ra = 8.63 nm

Figure 5: Measurement of Nanoroughness using Atomic Force Microscopy.

3 SUPPLEMENTARY DISCUSSION

3.1 Polymer Dynamics and Self-DiffusionPolymer melts are an equilibrium system and their mobility is commonly described bythe models of Rouse, reptation, etc. The fundamental dynamic property that charac-terizes the average motion of a polymer chain is the coefficient of self-diffusion (D).Typical values of self-diffusion coefficients from the literature are listed in Table 3.

Table 3: A Short Summary of Self-Diffusion Coefficient (D) from literature. Tmand Tg stand for melting and glass transition temperature, respectively.

Ref. Polymer Mol. Wt. Temp. D Comments(g/mol) (K) (m2/s)

[7] Linear H-PB 5×104 – 20 × 104 398.15 10−14 – 5×10−16 Tm ∼ 381.15 K[10, 8] Polyisoprene 560 – 9.82× 104 373.15 2.2×10−10 – 1.0×10−14 Tg ∼ 192 K [3]

[10] Polybutadiene 690 – 4.99×104 373.15 7.0×10−11 – 2.0×10−14 Tg ≤ 183.15 K[19] Polyethylene 200 – 12×104 448.15 6.6×10−10 – 1.3×10−14 Tm∼ 353.15 – 400.15 K[16] PDMS 500 – 5×105 293.65 7.0×10−10 – 5× 10−15 Tg ∼ 150.15 K[9] PS 600 – 19×103 487.8 2.5×10−10 – 1.5× 10−13 Tg ∼ 333.15 – 373.15 K

5

3.2 Stress-Induced Molecular Mobility and Plastic-Deformation

Confidential 1

A B C

Surrounding polymer chains

Polymer chain in surrounding elastic-media

ShearStress Relaxation

(a)

Confidential 2

Plastic Relaxation

oF

F

γ

A

B

C

Reduced

Barr

ier

localγ plasticγ

(b)

Confidential 1

f

V

)/( Vn f

T

Shear

Stress

(c)

Figure 6: Mechanism of plastic deformation and shear transformation in glassypolymers [5]. (a) A unit shear transformation in a kinetically trapped state undershear stress comprises of an initial elastic shear-strain which is followed by plastic-relaxation of polymer chain segments. (b) Free energy landscape, associated witha polymer chain, during a unit shear transformation (c) Accumulation of severalshear transformations leads to macroscopic plastic deformation.

As stated in the main letter, plastic deformation in polymers at a continuum scaleis understood in terms of shear transformations i.e. events of spatial rearrangements ofmolecular clusters causing stress-relaxation. Consider the scenario shown in the Figure6: well below Tg, the polymer chains are kinetically trapped in their local configura-tions and timescales for mobility (specifically translation motions) of these chains are

6

extremely large. However, application of shear-stress on the material element causesits deformation and the polymer chain under consideration changes its orientation: firstelastically, and then due to some local perturbation it relaxes plastically while over-coming the potential barrier set up due to neighboring molecules. Thus, qualitativelyspeaking, the application of stress enhances the mobility of the polymer chain as itrelaxes, and changes its configuration on experimental time scales. Effects of such cu-mulative events during active plastic deformation characterize the enhanced dynamicsin deforming glasses below Tg.

3.3 Temperature Rise Due to Plastic DeformationAs an illustration, we measured the specific heat of E3/E15 in 1:1-42.3%PEG filmthrough differential scanning calorimetry, as shown in Figure 7. From the rate of heatflow into the sample and specified rate of temperature rise during thermal scan the Cpis obtained as 1860 J/Kg-K, and the density was measured to be ρ = 1180 Kg/m3.Based on the stress-strain curves, if we estimate the flow stress for plastic deformationto be σ f = 8 MPa, then for a plastic strain of εp = 0.5, a simple estimate of adiabatictemperature rise is:

4T =σ f εp

ρCp= 3.6◦C.

As seen here, the temperature rise, even according to fully adiabatic analysis, isquite small. External work due to the application of stresses leads to mechanically-assisted (and not temperature assisted) enhanced mobility of polymer chains (or seg-ments).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

40 50 60 70 80 90 100

Hea

t Fl

ow

(W

/g)

Temperature (oC)

Figure 7: DSC scan of E3/E15 in 1:1-42.3% PEG film.

7

4 Bonding Experiments

4.1 Roll-Bonding Machine

Rollers

Pulley System

Motor

Position Handle

Springs

Load Cell

Threaded Rod

2’’

Figure 8: A roll-bonding machine to carry out sub-Tg, solid-state, plasticity-induced bonding. For more details see [17].

Figure 8 shows a CAD model of the roll-bonding machine designed for this work.The machine is capable of achieving different levels of plastic strain by adjustmentof the gap between the rollers and monitoring the compression load during rolling.The angular speed of the rollers is controlled using a stepper motor. The radius of therollers (R) is 100 mm, much larger than the total initial thickness of a film-stack (t1),which is typically less than 1 mm. The incoming stack of film behaves like a thin stripand through-thickness plastic deformation is triggered under such conditions. Fromkinematics of rigid-plastic rolling of thin-strip [12] the time spent during active plasticdeformation can be estimated as follows:

τ =

√R(t1− t2)

V2. (1)

In the above equation, t1 is the initial thickness of film-stack, t2 is the thickness offilm-stack at the exit, V2 is the linear speed at the exit. For V2 = 5.23 mm/s, t1=0.6 mmand t2=0.45 mm (indicating 25% nominal plastic strain), the time spent by a materialelement under the roller would be approximately 0.74 s. This is how we achieve sub-Tg, solid-state, plasticity-induced roll-bonding in a period of time on the order of asecond. The Supplementary video S1 demonstrates how a stack of films with a certaininitial thickness is subjected to active plastic straining leading to sub-Tg, solid-state,plasticity-induced bonding. The final thickness of the roll-bonded stack is less than theinitial. Complete details on the roll-bonding machine and process are available in [17].

8

0.5’’

Figure 9: Peel-Test in mechanical tester to determine mode-I fracture toughness(Gc).

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 20 40 60 80 100 120 140

Load

(N

)

Displacement (mm)

Figure 10: Force versus displacement curve during Peel-Test. In the steady-statepeeling the peel-force becomes steady with respect to cross-head displacement.

9

Table 4: For a given exit speed (V2 = 5.23 mm/sec) and an initial thickness t1 = 0.6mm, estimates of time spent under the roller bite during plastic straining.

Plastic Strain t2 Time(mm) (seconds)

0.05 0.57 0.330.1 0.54 0.470.15 0.51 0.570.20 0.48 0.660.25 0.45 0.74

4.2 Peel TestFigure 9 shows a snapshot of the peel test. A peel test fixture was designed to performaccurate mode-I fracture testing. Such a test is also commonly known as T-peel testin the literature. The designed fixture [17, 18], provides support to a long tail of thepeel-specimen and eliminates any spurious effects due to gravity. The Supplementaryvideo S4 gives an illustration on how the peel tests were conducted (also see [18] formore details).

When a stack of six layers is roll-bonded, a total of five bonded interfaces areformed. Peeling is done at the central interface. Figure 10 shows force versus dis-placement curve during a peel test. For all peel tests a cross-head speed of 15 mm/minwas chosen. The steady-state peeling force P is used to estimate the rate of externalwork per unit advance of crack as 2P/b, where ‘b’ is the width of the specimen (typi-cally 15 – 20 mm). In order to correctly determine the fracture toughness (Gc) of theplastically-welded interface, any amount of plastic work due to bending of peel armsmust be subtracted from the total steady state work [15].

Since glassy polymers may exhibit both kinematic and isotropic hardening, wemeasured their yield strength in tension after the roll-bonding (at different levels ofbonding strain). As an illustration, Figure 11 shows the true stress-strain curves in ten-sion for E15-alone-42.3% PEG films roll-bonded at different levels of nominal plasticstrain. It is seen that yield points of films in tension after roll-bonding at differentlevels of plastic strain are not much different than the yield point of the starting film.This indicates that effect of plastic strain, during roll-bonding, on the yield strength ofthe films is negligible, and therefore there is no special need to use a modified yieldstrength for analyses in mechanics of peel test. A detailed illustration is provided in[17]. The error bars in Gc (as shown in the main letter) are based on the variation whenpeeling force becomes steady.

4.3 Lap-Shear TestingPreparation of lap specimens and shear-strength measurements were carried out in In-stron testing machine. A lap joint was assembled between two film layers, each layerbeing nearly 100 µm thick. The overlapping region was nearly A = 5×5 = 25 mm2 inarea. A cross-head speed of 0.5 mm/min was chosen to apply desired compression load

10

0

5

10

15

20

25

30

35

40

45

0 0.2 0.4 0.6 0.8 1

Stre

ss (

MP

a)

Strain

E15-alone-42.3% PEG

E15-alone-42.3% PEG, 11.4% plastic strain



Figure 11: True stress-strain curves under tension for E15-alone-42.3% PEG, af-ter roll-bonded at different levels of nominal plastic strain.

2’’Lap joint

Failure

Figure 12: Lap shear-strength test specimen in tensile tester.

on the overlapping area. The sample was plastically bonded by pressing between twoparallel (accuracy: 1 µm) flats. Lap joint was tested for shear-strength in tension mode(at a cross-head speed of 15 mm/min). A snapshot of the test is shown in Figure 12.The peak force before failure divided by the bonded area was taken as the lap shear-strength. Figure 13 shows the force versus displacement during a lap shear-strengthmeasurement.

4.4 Mechanics of Axisymmetric UpsettingUnconstrained compression of a film stack with initial thickness much smaller than theradius of the stack qualifies as a classic case of an upsetting problem. As shown in theSupplementary video S2-a, a film stack with an initial thickness of 0.84 mm requirespeak loads up to 40 kN (which equates to a peak nominal stress of 78.9 MPa, muchlarger than yield strength of the polymer) in order to achieve a final thickness of 0.70

11

0

0.5

1

1.5

2

2.5

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Load

(N

)

Displacement (mm)

Figure 13: Force versus displacement curve during lap shear-strength testing. Forthis specimen a nominal plastic strain of 9.0% was imposed on an overlappingarea of 5 mm by 5 mm and the shear-strength (σs=Fmax/A) was estimated to be0.07 MPa.

mm due to compression. This can be attributed to radially-inward directed frictionalforces acting on the top and bottom surfaces during compression.

Figure 14 schematically shows the upsetting of a film stack. Figure 15 shows thestress components along with the frictional forces acting on a cylindrical element.

Figure 14: Axisymmetric Upsetting of laminates.

Here, we employ the upper bound analysis to predict the loads required to achieveplastic deformation in upsetting scenario and compare it with the experimentally notedloads. The analysis presented here is borrowed from [4, 13], where a detailed derivationcan also be found.

If ET is the total energy rate expended during material deformation, then ET =L×V [6], where L represents the forming load and V represents the velocity of the die.The total energy expended in material deformation itself can be expressed as sum ofenergy rates for deformation (ED) and frictional work (EF ):

ET = ED + EF (2)

The deformation energy rate is given as a volume integral of dissipation:

12

Figure 15: Stresses and frictional forces acting on an element during axisymmetricupsetting.

ED =∫

Vσ ˙εdV (3)

where σ is the flow stress for plastic deformation and ˙ε is the effective strain rate. ˙ε,in the present scenario of homogeneous axisymmetric deformation, is equal to VD/h(with VD being the speed of the die during compression and h the height of the stackat a particular instant). The rate of work due to frictional dissipation (EF ) includes thefriction energies on both the top and bottom surface of the deforming part and is givenas an integral of dissipation over the surfaces:

EF = 2∫

SFτvds (4)

where τ and v = (VD ·2πr/2h) denote the shear stress and radial velocity on the top andbottom surfaces. The shear stresses τ is assumed to be equal to mσ/

√3 (with m being

the friction factor). Computing the quantities in equations (3) and (4) and substitutingthem into (2), we arrive at the total energy rate:

ET = πR2σVD +

23

πmσ√3

VD

hR3.

Thus, the load is estimated as:

L =ET

VD= πR2

σ

(1+

23√

3m

Rh

). (5)

During upsetting to = 0.84 mm, t f = 0.7mm and therefore e= ln(to/t f )≈ 0.18, andloading occurred at a crosshead speed of 6 mm/min (leading to an estimate of nominalstrain rate of 0.13 sec−1). Figure 16 shows the strain-rate sensitivity measurements intension; from which a flow stress of σ= 10 MPa is estimated. Based on the assumptionof volume conservation during upsetting, the final radius (R) corresponding to t f = 0.7

13

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1

Stre

ss (

MPa

)

Strain

0.0025 sec-1

0.025 sec-1

0.25 sec-1

Figure 16: Strain-rate sensitivity of E3/E15 in 1:1-42.3% PEG. Nominal strain-rates are listed.

mm is estimated as 13.7 mm. By choosing an extreme value of m =1 and substitutingother quantities in equation (5), we estimate the upper bound load L = 50.29 kN. Thus,it is clear that the friction plays a significant role, despite the use of Teflon, in enhancingthe loads required for bulk plastic deformation in ‘upsetting’ (where R/h >>1).

4.5 Mechanics of uniaxial strain die

33

11 22

Figure 17: A set-up to achieve uniaxial strain in compression.

As discussed in the main letter and Supplementary video S2, the purpose of design-ing a ‘uniaxial strain die’ was to explicitly show the role of active plastic deformationin achieving sub-Tg, solid-state, plasticity-induced bonding. Figure 17 shows the CADmodel of a ‘uniaxial strain die’. Such a setup is capable of generating large levels of

14

hydrostatic pressure, while strongly limiting the plastic flow to negligible levels, whena circular stack of film with a radius equal to the internal radius of the cavity is com-pressed inside the die.

We present a couple of analyses to demonstrate the principle of the ‘uniaxial straindie’. Illustrations related to deformation theory of plasticity, as presented here, areborrowed in parts from [11, 13]. In what follows next, a boldface letter is to used toindicate a tensor variable.

4.5.1 Elasticity Analysis

First, we consider axisymmetric elastic compression of a film stack placed in the die.Here, all strains are assumed to be elastic and frictional forces are assumed to be absent.The solution to this problem is derived from the standard procedure of stresses in athick-walled cylinder with a zero internal radius. A cylindrical coordinate system (r,Θ, z) is used. The principal stress components are denoted by σr, σΘ and σz, and theassociated strains given as εr, εΘ and εz. All other shear components are zero. Dueto axisymmetry and wall constraints inside the die we have σr = σΘ (= σ, say) andεr = εΘ = 0. Using the boundary constraints with the stress-strain relation of linearelasticity:

εεε =1+ν

Eσσσ− ν

Etr(σσσ)I, (6)

we find,

σz =E(1−ν)εz

(1−2ν)(1+ν)(7)

σ =Eνεz

(1−2ν)(1+ν)(8)

where, E and ν are Young’s modulus and Poisson’s ratio, respectively. The stress tensorin terms of principal directions er, eΘ and ez is given as σσσ = σ er⊗ er + σ eΘ⊗ eΘ + σzez⊗ ez. σσσ can be decomposed into deviatoric part (σσσ′) and hydrostatic part (σmI, withσm = (σr +σΘ +σz)/3 denoting the mean normal stress), and written as σσσ = σσσ′ + σmI.The von Mises stress (σv) is given as:

σv =

√32

σσσ′ : σσσ′ (9)

Thus, in the presence of die the von Mises stress (σv,die) and hydrostatic pressure(pdie =−σm) are given as:

pdie =E|εz|

3(1−2ν)(10)

σv,die =E|εz|1+ν

(11)

In contrast if we imagined axisymmetric, unconstrained elastic compression, with-out any frictional effects then we would have σz = Eεz, and σr = σΘ = 0. In such casethe von Mises stress (σv,no−die) and hydrostatic pressure (pno−die) would be given as:

15

pno−die =E|εz|

3(12)

σv,no−die = |σz| (13)

We emphasize that elasticity analysis is valid only up to the onset of plastic de-formation. However, if we are within the elastic limit then equations (10) and (12)show that large hydrostatic-pressure can build up during compression inside the die.Particularly in the limit as ν→ 0.5, pdie → ∞.

In the video S2-b part II, a maximum compressive load of 40 kN is applied on afilm-stack with radius 0.5′′= 12.5 mm; corresponding to σz =−78.98 MPa. Accordingto equation (7), if σz = −78.98 MPa, ν = 0.45, and E=300 MPa (approximated fromthe nominal strain rate of 0.13 sec−1, see Figure 16), then εz ≈ −0.12. Substituting|εz| = 0.12, E = 300 MPa and ν = 0.45 in equation (11), σv,die = 25.7 MPa. Clearly,σv,die thus obtained is larger than the yield strength of the film. This indicates thepossibility of plastic deformation even in the presence of the die. Next, we present ananalysis based on the incremental (or “flow theory”) of plasticity, which accounts forplastic deformation.

4.5.2 Incremental (“Flow Theory”) of Plasticity

Here, we take into account the plastic deformation and demonstrate how little amountof plastic straining occurs when a film stack is compressed in the presence of the ‘uni-axial strain die’ and is loaded to values of |σz|>> σyield .

The total strain increment tensor (dεεε) is taken as the sum of the elastic strain incre-ment tensor (dεεεe) and the plastic strain increment tensor (dεεεp):

dεεε = dεεεe +dεεε

p (14)

The increment in elastic strain tensor can be derived using equation (6) and writtenas:

dεεεe =

1+ν

Edσσσ′+

1−2ν

Ed(tr(σσσ))I (15)

Under multi-axial loading the behavior of ductile materials can be described by theLevy-Mises equations, which relate the principal components of strain increments inplastic deformation to the principal applied stresses (deviatoric components). In thepresent scenario this can be expressed as:

εrp

σ′r=

εΘp

σ′Θ

=εz

p

σ′z(16)

On the grounds of axisymmetric compression, similar to what was discussed in theprevious section, we have σr = σΘ (= σ, say), and therefore εr = εΘ (ε, say).

We further define following quantities to aid this illustration:

|σσσ′′′|=√

σσσ′′′ : σσσ′′′ (17)

16

σ =

√32

σσσ′′′ : σσσ′′′ =

√32|σσσ′′′| (18)

|dεεεp|=√

dεεεp : dεεεp (19)

dεp =

√23

dεεεp : dεεεp =

√23|dεεε

ppp||| (20)

The flow rule can be written as:

dεεεp

|dεεεp|=

σσσ′′′

|σσσ′|(21)

The total increment in plastic strain can be written as:

dεεεp =−1

2dε

pz er⊗ er−

12

dεpz eΘ⊗ eΘ +dε

pz ez⊗ ez (22)

It is worth noting that at any instance neither the directions nor the relative magni-tudes of plastic strain components change, and therefore we can write equation (22)as:

εεεp =−1

2ε

pz er⊗ er−

12

εpz eΘ⊗ eΘ + ε

pz ez⊗ ez (23)

By choosing DDD = − 12 er⊗ er− 1

2 eΘ⊗ eΘ + ez⊗ ez, we can re-write equation (23)as:

εεεp = ε

pz DDD (24)

In equation (24), εpz is negative during compression. Using the flow rule from

equation (21), and the fact that increments in plastic strains are proportional to theprincipal directions (which are constant throughout the deformation history); we canrewrite flow rule in terms of total plastic strain at any instant as:

εεεp

|εεεp|=

σσσ′

|σσσ′|(25)

If we assume plastic deformation to continue at a constant yield Y , then:

Y =

√32|σσσ′| (26)

It is worth mentioning that the yield strength of polymers is usually a function ofhydrostatic pressure and plastic strain (and the flow stress increases with increasinghydrostatic pressure and plastic strain, thus an assumption of constant yield stress is anunder estimation).

By combining equations (24), (25) and (26) we can write:

σσσ′ =

εpz

|εpz |

23

Y DDD (27)

17

Since εpz is negative during compression, equation (27) can be re-written as:

σσσ′ =−2

3Y DDD (28)

The elastic strain increments, as given in equation (15), occur both due to devia-toric stress and hydrostatic stress. At the onset of plastic flow (and continued plasticyielding at constant flow stress) the the deviatoric stress becomes constant (given byequation (27)), after which there is no further contribution to elastic strains due to de-viatoric stress components. However, the normal stress and the hydrostatic part of theelastic strains continue to increase. Thus, total elastic-strain can be written as:

εεεe =−(1+ν

E)(

2Y3)DDD+

σm

3(

1−2ν

E)I (29)

From equation (14), the total strain can be written as:

εεε = εpz DDD− (

1+ν

E)(

2Y3)DDD+

σm

3(

1−2ν

E)I (30)

Now imposing the constraint that total strains in the r and Θ direction are zero i.e.εr = εΘ = 0 then equation (30) implies:

σm

3=

E1−2ν

[ε

pz

2− Y (1+ν)

3E] (31)

Thus, the overall stress tensor can be written as:

σσσ =−2Y3

DDD+E

2(1−2ν)ε

pz I− Y (1+ν)

3(1−2ν)I (32)

If we again choose σz = -78.89 MPa (and same elastic constants as used in theprevious section), we now get the much-reduced estimate |εp

z | ≈ 0.023. We emphasizethe fact that in polymers the plastic straining is accompanied with hardening, and theyield stress increases with mean normal pressure, therefore, |εp

z | = 0.023 is an overesti-mation of axial plastic strain from this loading of the ‘uniaxial strain die’, even thoughthe applied axial stress was more than an order of magnitude greater than the yieldstrength.

Lastly, the ratio σrσz

= 0.96 which suggests that the state of stress inside the die is‘hydrostatic’.

These calculations demonstrate that despite the large hydrostatic pressures there isonly small plastic straining, due to which no bonding outcome is noted.

5 Supplementary ResultsHere we present additional and supporting experimental data (Gc and lap shear-strengthresults) on three films made from E3-alone-42.3% PEG, E3/E15 in 1:1-42.3% PEG andE15-alone-42.3% PEG, and report reproducible trends on the bonding results. Sinceeach set of bonding experiment has been carried out on films made from a particularbatch of raw materials and solvents obtained commercially, their mixing, and drying

18

via solvent casting, we refrain from merging all the data owing to any inherent varia-tion that may be present due to these factors. Figures 18(a) and 18(b) show Gc trendsfor the three films based on second and third trials corresponding to the two additionalbatches of material films prepared. Similarly, Figures 19(a) and 19(b) show lap shear-strength measurements for bonding experiments based on second and third batches ofmaterials. Excellent reproducibility in the bonding trends and non-monotonic correla-tion of Gc and lap shear-strength with plastic strain is noted, and conclusively estab-lishes the new phenomenon of sub-Tg, solid-state, plasticity-induced bonding.

We also report a sample result showing the effect of strain-rate in rolling experi-ments on films made from E3/E15 in 1:1-42.3% PEG. Two roller speeds of 0.5 rev/minand 0.05 rev/min, leading to exit speeds of 5.23 mm/s and 0.523 mm/s respectively,were selected to study the effect of strain-rate on roll-bonding. Since the time spentin rolling inversely depends on the exit speed (equation (1)), an order of magnitudedifference in the exit speeds would approximately amount to an order of magnitudedifference in rolling-times, and thus leading to an order of magnitude difference innominal strain-rate (given by (t1 − t2)/τ). Gc with respect to plastic strain for tworoller speeds is shown in Figure 20. We observe negligible effect of strain-rate onfracture toughnesses.

At slow to moderate strain-rates, when bonding processes are primarily isothermalthen negligible influence of strain-rate can be expected, because whenever adiabaticeffects (or any other factors) do not alter the micro-mechanism of plastic deforma-tion that leads to enhanced molecular mobility and interpenetration of polymer chainsacross the interface, then bonding is likely to depend directly on the gross plastic strain.Warren and Rottler [20] showed that accelerated dynamics in a deforming glass, underdifferent deformation settings which reflected varying strain-rates, directly correlatedwith net plastic strain.

6 Information on Supplementary VideosSupplementary video S1: Sub-Tg, solid-state, plasticity-induced roll-bonding of poly-meric films.

Supplementary video S2-a: Sub-Tg, solid-state, plasticity-induced bonding of film-stack during compression in upsetting experiment.

Supplementary video S2-b part I: Design of a ‘uniaxial-strain die’ (i.e. ‘hydrostaticdie’).

Supplementary video S2-b part II: Compression of film-stack in ‘uniaxial-strain die’.

Supplementary video S2-b part III: No-bonding outcome of film-stack after compres-sion in ‘uniaxial-strain die’.

Supplementary video S3: No-bonding outcome between an ‘elastic’ and ‘plastic’ film.

19

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45

Gc

(J/m

2)

Plastic-Strain (%)

E3-alone-42.3% PEG, reproducible trend 2

E3/E15 in 1:1-42.3% PEG, reproducible trend 2


(a)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45

Gc

(J/m

2)

Plastic-Strain (%)


E3/E15 in 1:1-42.3% PEG, reproducible trend 3


(b)

Figure 18: Reproducible trends for roll-bonding for three films, Gc with respectto plastic strain for second and third batch of materials prepared. Gc is calculatedbased on the mean steady-state peel force during peeling, and error bars in Gc arebased on one standard deviation from fluctuations in the peeling force in steady-state regime. Plastic-strain is calculated based on mean thicknesses before andafter bonding (10 measurements), and the error bars in plastic strain are derivedfrom these measurements.

Supplementary video S4: Peel-test on roll-bonded laminates.

20

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12 14 16 18 20

Lap

Sh

ear-

Stre

ngt

h (M

Pa)

Plastic Strain (%)


E3/E15 in 1:1-42.3%PEG, reproducible trend 2


(a)

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12 14 16 18 20

Lap

Sh

ear-

Stre

ngt

h (M

Pa)

Plastic Strain (%)


E3/E15 in 1:1-42.3%PEG, reproducible trend 3


(b)

Figure 19: Reproducible trends for lap shear-strength (σs [MPa]) with respect toplastic strain. Plastic-strain is calculated based on mean thicknesses before andafter bonding (10 measurements), and the error bars in plastic strain are derivedfrom these measurements.

21

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35

Gc

(J/m

2)

Plastic-Strain (%)

E3/E15 in 1:1-42.3% PEG, roller speed 0.5 rev/min

E3/E15 in 1:1-42.3%PEG, roller speed 0.05 rev/min

Figure 20: Effect of strain-rate on Gc with respect to plastic strain.

22

References[1] Methocel cellulose ethers in aqueous systems for tablet coating. http://www.dow.com/scripts/

litorder.asp?filepath=/198-00755.pd.

[2] Methocel molecular weight viscosity relationship. http://dowwolff.custhelp.com/app/answers/detail/a_id/1316.

[3] Segmental and chain dynamics in amorphous polymers. http://comse.chemeng.ntua.gr/segmdyn_polpage.htm.

[4] Taylan Altan, Gracious Ngaile, and Gangshu Shen. Cold and hot forging: fundamentals and applica-tions, volume 1. ASM international, 2005.

[5] Ali S Argon. The physics of deformation and fracture of polymers. Cambridge University Press, 2013.

[6] B Avitzur. Metal forming: processes and analysis, 1968.

[7] Craig R Bartels, Buckley Crist, and William W Graessley. Self-diffusion coefficient in melts of linearpolymers: chain length and temperature dependence for hydrogenated polybutadiene. Macromolecules,17(12):2702–2708, 1984.

[8] M Doxastakis, DN Theodorou, G Fytas, F Kremer, R Faller, F Muller-Plathe, and N Hadjichristidis.Chain and local dynamics of polyisoprene as probed by experiments and computer simulations. TheJournal of chemical physics, 119(13):6883–6894, 2003.

[9] Gerald Fleischer. Temperature dependence of self diffusion of polystyrene and polyethylene in themelt an interpretation in terms of the free volume theory. Polymer Bulletin, 11(1):75–80, 1984.

[10] Gerald Fleischer and Matthias Appel. Chain length and temperature dependence of the self-diffusionof polyisoprene and polybutadiene in the melt. Macromolecules, 28(21):7281–7283, 1995.

[11] Morton E Gurtin, Eliot Fried, and Lallit Anand. The mechanics and thermodynamics of continua.Cambridge University Press, 2010.

[12] Kenneth Langstreth Johnson. Contact mechanics. Cambridge university press, 1987.

[13] William Johnson and Peter Bassindale Mellor. Engineering plasticity. Horwood, 1983.

[14] CM Keary. Characterization of methocel cellulose ethers by aqueous sec with multiple detectors.Carbohydrate polymers, 45(3):293–303, 2001.

[15] Kyung Suk Kim and N Aravas. Elastoplastic analysis of the peel test. International Journal of Solidsand Structures, 24(4):417–435, 1988.

[16] R Kimmich, W Unrath, G Schnur, and E Rommel. Nmr measurement of small self-diffusion co-efficients in the fringe field of superconducting magnets. Journal of Magnetic Resonance (1969),91(1):136–140, 1991.

[17] Nikhil Padhye. Sub-Tg, Solid-State, Plasticity-Induced Bonding of Polymeric Films and ContinuousForming. PhD thesis, Massachusetts Institute of Technology, Cambridge, 2015.

[18] Nikhil Padhye, David M. Parks, Alexander H. Slocum, and Bernhardt L. Trout. Enhancing the perfor-mance of the t-peel test for thin and flexible adhered laminates. Review of Scientific Instruments, 87(8),2016.

[19] DS Pearson, G Ver Strate, E Von Meerwall, and FC Schilling. Viscosity and self-diffusion coefficientof linear polyethylene. Macromolecules, 20(5):1133–1141, 1987.

[20] Mya Warren and Jorg Rottler. Microscopic view of accelerated dynamics in deformed polymer glasses.Physical review letters, 104(20):205501, 2010.

23

a new phenomenon: sub-tg, solid-state, plasticity …web.mit.edu/npdhye/www/padhye-nature-2017.pdfa...

Documents